Problem: Rewrite as a simplified fraction. ${3.5\overline{3} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{aligned}100x &= 353.3333...\\ 10x &= 35.3333...\end{aligned}}$ Subtracting the two equations, we have: ${90x = 318}$ ${x = \dfrac{318}{90}} $ ${x = \dfrac{53}{15}} \text{or} {3 \dfrac{8}{15}}$